Multi-horizon uniform superior predictive ability revisited

Monschang, Verena; Trede, Mark; Wilfling, Bernd

Abstract

This paper examines the joint-hypothesis-testing problem that arises when comparing two competing forecast methods across multiple horizons. We focus on the concept of uniform Superior Predictive Ability (uSPA) and investigate the asymptotic properties of the corresponding test statistic. Under standard regularity conditions, the asymptotic distribution under the null hypothesis is derived, ensuring that the test maintains the correct size and exhibits consistency. Monte Carlo simulations are used to assess the test's finite-sample performance. An empirical application replicates and extends earlier studies, providing inference for multi-horizon comparisons between direct and iterative forecasting approaches.

Keywords
Forecast evaluation; joint-hypothesis testing; direct versus iterative forecasts